A Simulation-Based Specification Test for Diffusion Processes
A Simulation-Based Specification Test for Diffusion Processes
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DOI：
10.1198/073500107000000412
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发表时间：
2008-04
影响因子：
3
通讯作者：
Geetesh Bhardwaj;V. Corradi;Norman R. Swanson
中科院分区：
文献类型：
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作者：
Geetesh Bhardwaj;V. Corradi;Norman R. Swanson
本文有两个贡献。首先，我们概述了一个简单的基于模拟的框架，用于在条件密度的函数形式未知的情况下构建多因素和多维扩散过程的条件分布。例如，在给定直到周期 t 的信息的情况下，这些分布可用于形成时间周期 t + τ 的预测置信区间。其次，我们使用基于模拟的方法来构建扩散过程正确规范的测试。建议的测试符合安德鲁斯条件柯尔莫哥洛夫测试的精神。然而，在当前上下文中，零条件分布是未知的，并且被其模拟对应分布所取代。检验统计量的极限分布不是无干扰参数的。鉴于此，通过适当使用块引导程序可以获得渐近有效的临界值。与使用边际分布/密度构建的测试相比，建议的测试对更大类别的替代方案具有威力。小型蒙特卡罗实验的结果强调了所提出的测试的良好有限样本属性，并且实证例证强调了所提出的模拟和测试方法的易于应用。
This article makes two contributions. First, we outline a simple simulation-based framework for constructing conditional distributions for multifactor and multidimensional diffusion processes, for the case where the functional form of the conditional density is unknown. The distributions can be used, for example, to form predictive confidence intervals for time period t + τ, given information up to period t. Second, we use the simulation-based approach to construct a test for the correct specification of a diffusion process. The suggested test is in the spirit of the conditional Kolmogorov test of Andrews. However, in the present context the null conditional distribution is unknown and is replaced by its simulated counterpart. The limiting distribution of the test statistic is not nuisance parameter-free. In light of this, asymptotically valid critical values are obtained via appropriate use of the block bootstrap. The suggested test has power against a larger class of alternatives than tests that are constructed using marginal distributions/densities. The findings of a small Monte Carlo experiment underscore the good finite sample properties of the proposed test, and an empirical illustration underscores the ease with which the proposed simulation and testing methodology can be applied.